Question

If an article is sold for Rs.178 at a loss of 11%. What should be its selling price in order to earn a profit of 11%?
A. Rs.222.50
B. Rs.267
C. Rs.222
D. Rs.220

Answer 1

Hint: First of all, find out the cost price of the article by using the given data and the formula \[{\text{C}}{\text{.P}} = \dfrac{{{\text{S}}{\text{.P}}}}{{100 - {\text{Loss% }}}} \times 100\]. Then find out the selling with a profit of 11% by using the formula \[{\text{S}}{\text{.P}} = \dfrac{{100 + {\text{Profit% }}}}{{100}} \times {\text{C}}{\text{.P}}\]. So, use this concept to reach the solution of the given problem.

Complete step-by-step answer:
Given that the article is sold for Rs.178 at a loss of 11%.
So, selling price of article = Rs.178
Loss percent = 11%
We know that \[{\text{C}}{\text{.P}} = \dfrac{{{\text{S}}{\text{.P}}}}{{100 - {\text{Loss% }}}} \times 100\]
So, cost price of the article \[ = \dfrac{{178}}{{100 - 11}} \times 100 = \dfrac{{178}}{{89}} \times 100 = 2 \times 100 = {\text{Rs}}.200\]
Now, we have to find the selling price of the article in order to get a profit of 11%
We know that, \[{\text{S}}{\text{.P}} = \dfrac{{100 + {\text{Profit% }}}}{{100}} \times {\text{C}}{\text{.P}}\]
So, selling price of the article to have profit of 11% \[ = \dfrac{{100 + 11}}{{100}} \times 200\]
                                                                                           \[
   = \dfrac{{111 \times 200}}{{100}} \\
   = 111 \times 2 \\
   = {\text{Rs}}{\text{.222}} \\
\]
Hence, to gain a profit of 11% the selling price should be Rs.222
Thus, the correct option is C. Rs.222

Note: There is a loss whenever the cost price of the article is greater than the selling price of the article. And there is a profit whenever the selling price of the article is greater than the cost price of the article.